General principles concerning the motion of fluids
Euler treats the motion of fluids on the same footing as in E225, dealing with the principles of the equilibrium of fluids; in fact, he uses many of the ideas, especially that of pressure, of E225 in this work. This paper contains some of the earliest remarks indicating the role of boundary conditions in determining the appropriate integral for a partial differential equation. He also assumes that the state of the fluid is known at a certain time, and he reduces all of the theory of the motion of fluids to a solution of certain analytic formulae. Euler proves that solutions of the equations of motion can exist even when the forces are such that equilibrium is impossible. He shows that the existence of a velocity-potential is a special circumstance by exhibiting counterexamples of simple vortex flows (the first appearance of such flows) and motions that we now know as generalized Poiseuille flows (this marks the first appearance of these flows in this generality). (based on Clifford Truesdell's introduction to Opera Omnia Series II, Volume 12.)
Original Source Citation
Mémoires de l'académie des sciences de Berlin, Volume 11, pp. 274-315.
Opera Omnia Citation
Series 2, Volume 12, pp.54-91.